The effect of magnetic field and donor impurity on electron spectrum in spherical core-shell quantum dot

Abstract

The effect of homogeneous magnetic field and location of donor impurity on the electron energy spectrum and distribution of its probability density in spherical core-shell quantum dot is investigated. In the framework of the effective mass approximation and rectangular infinitely deep potential well, the solutions of the Schrodinger equation are found using the matrix method. The wave functions are expanded over the complete set of exact functions obtained without the magnetic field and impurity.It is shown that when the induction of magnetic field increases, the ground state of electron in the nanostructure without impurity or on-center impurity is successively formed by the states with m = 0, −1, −2, … (Aharonov-Bohm effect). When donor impurity is located in the shell of the nanostructure the Aharonov-Bohm effect vanishes.The dependences of electron energy spectrum and its wave functions on the location of impurity, placed along the direction of magnetic field or perpendicularly to it, are studied. It is shown, that in the first case, the quantum states are characterized by the certain value of magnetic quantum number m and the expansion contains the wave functions of the states with it only. In the second case, the cylindrical symmetry of the problem is broken and the new quantum states are formed from the states with different values of all three quantum numbers n, l, m and electron energy spectrum weakly depends on the magnetic field induction.